Budapest is full of hotels in a wide range of quality and price.
The closest hotel is the Danubius Hotel Gellert. Although it is 4-star hotel, be aware that it is mostly because of its termal-bath that can be freely used for the guests. Economy rooms interior has rather a 2-star fashion, however superior rooms are renovated in the last years.
I recommend you to search your favorite hotel engine or use this setup: City-center, rates between 75 and 124 euros, Sept. 24-27 where you can use the "View map" on the up-left corner, or similarly this setup: Gellert Hill, rates between 75 and 124 euros, Sept. 24-27
Personally, I would choose Residence Baron Hotel, although I've never been there.